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I need to compare two linear regression models that include the regressors in levels and in squares:

$Y=a_1x^2+b_1x+c_1$ and $Y=a_2x^2+b_2x+c_2 $

Specifically, I need to test whether these regression models are significantly different (i.e., whether $a_1=a_2,b_1=b_2,c_1=c_2$).

In the forum, I read that one should build respective interactions.

Yet, I do not exactly understand what is meant by including “interactions.”

What would that model look like? What should be compared with what, and what test statistic is best?

(I do not know Stata, unfortunately.)

Please advise.

Both models are based on /using the exact same population.

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    $\begingroup$ Are the two models run on the same population? Is Y the same? Is X? (it would help to use subscripts on Y and X to distinguish them). $\endgroup$ – Peter Flom Jan 9 '14 at 15:16
  • $\begingroup$ What did you read where? What was the context? $\endgroup$ – Glen_b Jan 10 '14 at 12:44
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As far as I know, model comparison should only be done on the same dataset. For models with different configurations, you can try Akaike information criterion (AIC) or Bayesian information criterion (BIC).

Your 2 models have the same regressors but different coefficients. The easiest thing to do is to check the confidence intervals for overlapping. For example, if CI of $a_1$ overlaps CI of $a_2$ or covers $a_2$ if only one model is fit, then there is no significant difference between them. You can do this for all 3 coefficients.

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